Formula:KLS:09.08:24: Difference between revisions

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{{DISPLAYTITLE:Formula:KLS:09.08:24}}
{{DISPLAYTITLE:Formula:KLS:09.08:24}}
<div id="drmf_head">
<div id="drmf_head">
<div id="alignleft"> << [[Formula:KLS:09.08:23|Formula:KLS:09.08:23]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:21|Formula:KLS:09.08:21]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:24|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:24|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:25|Formula:KLS:09.08:25]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:25|Formula:KLS:09.08:25]] >> </div>
</div>
</div>


<br /><div align="center"><math>{\displaystyle  
<br /><div align="center"><math>{\displaystyle  
\frac{\pochhammer{\beta}{n}}{n!}\Meixner{n}@{x}{\beta}{c}=\Jacobi{\beta-1}{-n-\beta-x}{n}@{(2-c}c^{-1})
\Ultra{\lambda}{n}@{x}=\sum_{\ell=0}^{\lfloor n/2\rfloor}\frac{(-1)^{\ell}\pochhammer{\lambda}{n-\ell}}
{\ell!\;(n-2\ell)!} (2x)^{n-2\ell}
}</math></div>
}</math></div>


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== Symbols List ==
== Symbols List ==


<span class="plainlinks">[http://dlmf.nist.gov/5.2#iii <math>{\displaystyle (a)_n}</math>]</span> : Pochhammer symbol : [http://dlmf.nist.gov/5.2#iii http://dlmf.nist.gov/5.2#iii]<br />
<span class="plainlinks">[http://dlmf.nist.gov/18.3#T1.t1.r5 <math>{\displaystyle C^{\mu}_{n}}</math>]</span> : ultraspherical/Gegenbauer polynomial : [http://dlmf.nist.gov/18.3#T1.t1.r5 http://dlmf.nist.gov/18.3#T1.t1.r5]<br />
<span class="plainlinks">[http://dlmf.nist.gov/18.19#T1.t1.r9 <math>{\displaystyle M_{n}}</math>]</span> : Meixner polynomial : [http://dlmf.nist.gov/18.19#T1.t1.r9 http://dlmf.nist.gov/18.19#T1.t1.r9]<br />
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:sum <math>{\displaystyle \Sigma}</math>]</span> : sum : [http://drmf.wmflabs.org/wiki/Definition:sum http://drmf.wmflabs.org/wiki/Definition:sum]<br />
<span class="plainlinks">[http://dlmf.nist.gov/18.3#T1.t1.r3 <math>{\displaystyle P^{(\alpha,\beta)}_{n}}</math>]</span> : Jacobi polynomial : [http://dlmf.nist.gov/18.3#T1.t1.r3 http://dlmf.nist.gov/18.3#T1.t1.r3]
<span class="plainlinks">[http://dlmf.nist.gov/5.2#iii <math>{\displaystyle (a)_n}</math>]</span> : Pochhammer symbol : [http://dlmf.nist.gov/5.2#iii http://dlmf.nist.gov/5.2#iii]
<br />
<br />


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<br /><div id="drmf_foot">
<br /><div id="drmf_foot">
<div id="alignleft"> << [[Formula:KLS:09.08:23|Formula:KLS:09.08:23]] </div>
<div id="alignleft"> << [[Formula:KLS:09.08:21|Formula:KLS:09.08:21]] </div>
<div id="aligncenter"> [[Jacobi#KLS:09.08:24|formula in Jacobi]] </div>
<div id="aligncenter"> [[Jacobi:_Special_cases#KLS:09.08:24|formula in Jacobi: Special cases]] </div>
<div id="alignright"> [[Formula:KLS:09.08:25|Formula:KLS:09.08:25]] >> </div>
<div id="alignright"> [[Formula:KLS:09.08:25|Formula:KLS:09.08:25]] >> </div>
</div>
</div>

Revision as of 00:34, 6 March 2017


Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Ultra{\lambda}{n}@{x}=\sum_{\ell=0}^{\lfloor n/2\rfloor}\frac{(-1)^{\ell}\pochhammer{\lambda}{n-\ell}} {\ell!\;(n-2\ell)!} (2x)^{n-2\ell} }}

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C^{\mu}_{n}}}  : ultraspherical/Gegenbauer polynomial : http://dlmf.nist.gov/18.3#T1.t1.r5
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a)_n}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 9.8 of KLS.

URL links

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